Comparison of deterministic and stochastic SIRS epidemic model with saturating incidence and immigration

Arabian Journal of Mathematics

Volumn 4, Issue 2, 2015, Pages 101-116

  Lahrouz, Aadil ^a   Omari, Lahcen ^a   Settati, Adel ^b   Belmaâti, Aziza ^c  

^a SIDI MOHAMED BEN ABDELLAH UNIVERSITY   (Morocco)

^b ABDELMALEK ESSAADI UNIVERSITY   (Morocco)

^c HASSAN II UNIVERSITY OF CASABLANCA   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85016084605     PISSN: 21935343     EISSN: 21935351     Source Type: Journal    
DOI: 10.1007/s40065-014-0119-0     Document Type: Article

References (22)

1. Beretta E., Takeuchi Y.: Global stability of a SIR epidemic model with time delay. J. Math. Biol. 33, 250–260 (1995)
2. Beretta E., Kolmanovskii V., Shaikhet L.: Stability of epidemic model with time delay ifluenced by stochastic perturbations. Math. Comp. Simul. 45, 269–277 (1998)
3. Brauer, F.; van den Driessche, P.: Models for transmission of disease with immigration of infective. Math. Biosci. 171, 143–154 (2001)
4. Brauer, F.; van den Driessche, P.; Wu, J.: Mathematical Epidemiology, Springer, Berlin (2008)
5. Capasso V., Serio G.: A generalization of the Kermack–McKendrick deterministic epidemic model. Math. Biosci. 42, 41–61 (1978)
6. Carletti M.: Mean-square stability of a stochastic model for bacteriophage infection with time delays. Math. Biosci. 210, 395–414 (2007)
7. Dalal, N.; Greenhalgh, D.; Mao, X.: A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325, 36–53 (2007)
8. Imhof L., Walcher S.: Exclusion and persistence in deterministic and stochastic chemostat models. J. Differ. Equ. 217, 26–53 (2005)
9. Kermack, W.O.; McKendrick, A.G.: Contribution to mathematical theory of epidemics. P. Roy. Soc. Lond. A Mat. 115, 700–721 (1927)
10. Liu, W.; Levin, S.A.; Iwasa, Y.: Influence of nonlinear incidence rates upon behavior of SIRS epidemiological models. J. Math. Biol. 23, 187–204 (1986)
11. Lyapunov, A.M.: The General problem of the stability of motion. Taylor and Francis, London (1992)
12. Li, X.; Jiang, D.; Mao, X.: Population dynamical behavior of Lotka–Volterra system under regime switching. J. Comput. Appl. Math. 232, 427–448 (2009)
13. Lahrouz A., Omari L., Kiouach D.: Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model, Nonlinear Anal. Model. Control 16, 59–76 (2011)
14. Lahrouz A., Omari L., Kiouach D., Belmaati A.: Deterministic and stochastic stability of a mathematical model of smoking. Stat. Probab. Lett. 81, 1276–1284 (2011)
15. Mena-Lorca, J.; Hethcote, H.W.: Dynamic models of infectious diseases as regulator of population sizes. J. Math. Biol. 30 693–716 (1992)
16. Mao, X.: Stochastic Differential equations and applications. Horwood Publishing Limited, Chichester. (1997)
17. Øksendal, B.: Stochastic differential equations an introduction with applications. Springer, New York (2000)
18. Shim E.: A note on epidemic models with infective immigrants and vaccination. Math. Biosci. Eng. 3, 557–566 (2006)
19. van den Driessche, P.; Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)
20. World Health Organization. The world health report 2002 reducing risks, promoting healthy life. http://www.who.int/whr/2002/en/whr02_en (2002)
21. Wang W., Ruan S.: Simulating the SARS outbreak in Beijing with limited data. J. Theor. Biol. 227, 369–379 (2004)
22. Zhou, Y.; Khan, K.; Feng, Z.; Wu, J.: Projection of tuberculosis incidence with increasing immigration trends. J. Theor. Biol. 254, 215–228 (2008)